Intriguing interfacial characteristics of the CS contact with MX2 (M = Mo, W; X = S, Se, Te) and MXY ((X ≠ Y) = S, Se, Te) monolayers

Using (hybrid) first principles calculations, the electronic band structure, type of Schottky contact and Schottky barrier height established at the interface of the most stable stacking patterns of the CS–MX2 (M = Mo, W; X = S, Se, Te) and CS–MXY ((X ≠ Y) = S, Se, Te) MS vdWH are investigated. The electronic band structures of CS–MX2 and CS–MXY MS vdWH seem to be simple sum of CS, MX2 and MXY monolayers. The projected electronic properties of the CS, MX2 and MXY layers are well preserved in CS–MX2 and CS–MXY MS vdWH. Their smaller effective mass (higher carrier mobility) render promising prospects of CS–WS2 and CS–MoSeTe as compared to other MS vdWH in nanoelectronic and optoelectronic devices, such as a high efficiency solar cell. In addition, we found that the effective mass of holes is higher than that of electrons, suggesting that these heterostructures can be utilized for hole/electron separation. Interestingly, the MS contact led to the formation of a Schottky contact or ohmic contact, therefore we have used the Schottky Mott rule to calculate the Schottky barrier height (SBH) of CS–MX2 (M = Mo, W; X = S, Se, Te) and CS–MXY ((X ≠ Y) = S, Se, Te) MS vdWH. It was found that CS–MX2 (M = Mo, W; X = S, Se, Te) and CS–MXY ((X ≠ Y) = S, Se, Te) (in both model-I and -II) MS vdWH form p-type Schottky contacts. These p-type Schottky contacts can be considered a promising building block for high-performance photoresponsive optoelectronic devices, p-type electronics, CS-based contacts, and for high-performance electronic devices.


Introduction
Aer the successful synthesis of graphene, 1 other two dimensional (2D) materials, such as hexagonal boron nitrides (h-BN), 2 transition metal dichalcogenides (TMDCs), 3 MXenes, 4 silicene, 5 germanene, 6 blue and black phosphorene, 7 borophene 8 and stanene, 9 have gained considerable attention in a new generation of optoelectronic and spintronic devices. 10 In the family of 2D materials, TMDCs with MX 2 (M ¼ transition metal atoms, X ¼ chalcogen atoms) stoichiometry have interesting physical/ chemical properties which arise due to the structural transition from multilayers to monolayers, for example an indirect to direct bandgap transition, 11 large exciton binding energy, 12 and an abundance of multiexcitons. 13 But a strong excitonic effect with high binding energies results in a very fast recombination rate of photogenerated electron and hole carriers in these materials (MX 2 monolayers), hence leading to a low quantum efficiency. 14 Therefore, abundant efforts have been made to tune and improve the chemical and physical properties of MX 2 monolayers. Another class of 2D materials, XY (X ¼ C, Si, Ge, Sn; Y¼ O, S, Se, Te), which exhibit planar structures 15 with sixteen (CY, SiY, GeY and SnY; Y¼ O, S, Se and Te) possible combinations, consisting of an equal number of two different atoms, have attracted much attention due to their stable conguration. 16 For each of these 2D binary monolayers, there are three different possible geometrical congurations, the puckered, buckled and planar structures. The hexagonal planar structure supports sp 2 hybridization, whereas the favorable hybridization in group V monolayers (phosphorene and arsenene) is sp 3 , which shows that the hybridization in group IV-VI binary monolayers is similar to those of phosphorene and arsenene. It is observed that CS monolayers in the planar conguration are metallic due to the strong overlap of the conduction and valence bands. 15 Lu (Zhang) et al. 17 ( 18 ) have selenized (sulfurized) MoS 2 (-MoSe 2 ) through a chemical vapor deposition (CVD) technique and named these Janus transition metal dichalcogenides (JTMDCs) with the chemical formula MXY (M ¼ Mo, W; (X s Y) ¼ S, Se). These materials have been shown to be promising for spintronic devices due to the SOC-induced Rashba spin splitting. 19 Using density functional theory (DFT) calculations, Xia et al. 20 showed that the atomic radius and electronegativity differences of the X and Y chalcogen atoms in MXY (M ¼ Mo, W; X, Y ¼ S, Se, Te) monolayers are associated with the direct to indirect bandgap transition and induced dipole moment. Furthermore, Idrees et al. 21 have also used DFT and shown that MoSSe, WSSe, MoSeTe and WSeTe (MoSTe and WSTe) monolayers are direct (indirect) bandgap semiconductors. They transformed indirect MoSTe and WSTe to direct bandgap semiconductors by using external electric elds. They have also investigated the absorption spectra, absorption efficiency, and photocatalytic behavior of these materials.
The stacking of isolated 2D materials via van der Waals forces in a precisely controlled sequence produces van der Waals heterostructures (vdWH). 22 This provides a versatile platform for exploring the uses of new phenomena in designing novel nanoelectronic devices. 23,24 In this regard, the stackings of semiconductors with semiconductors (SS contact) and metals with semiconductors (MS contact) are of crucial importance, with a wide range of device applications. 25 To date, many of the vdWH in the form of SS contacts have been investigated both theoretically [26][27][28][29][30][31][32][33][34][35][36][37] and experimentally [38][39][40][41] for novel extraordinary applications in optoelectronic devices. [42][43][44][45][46][47] In the case of MS contacts, the Schottky barrier (SB) is an energy barrier across the junction for the transport of carriers. 48 It reduces the contact resistance, modulates carrier polarity in the channel for transistors, and also enhances the selectivity of carrier extraction for photovoltaic cells, 49,50 hence it plays a key role in device performance. In MS contacts, there is another important phenomena, the Fermi level pinning (FLP) caused by metal-induced gap states (MIGS) and interface dipoles or defects created at the interface. 51 It refers to the insensitivity of the SB to the work function of the metal. 52 TMDCs have been used in almost every MS contact in both experiments 53,54 and theory. 55,56 The contact of single layer MoS 2 (semiconductor) has already been proposed with Ti (metal) 57 and other metals of varying work functions. 58 Indeed, the small lattice mismatch and identical symmetry of CS, MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and MXY ((X s Y) ¼ S, Se, Te) monolayers allow the creation of MS contacts in the form of CS-MX 2 and CS-MXY vdWH. Alternative ordering of the chalcogen atoms allows the creation of two models of the CS-MXY vdWH. Therefore, we have fabricated the possible stacking patterns in CS-MX 2 and in both (two) models of CS-MXY MS vdWH. Aer making the possible stacking congurations, we have investigated the electronic band structure, type of Schottky contact and Schottky barrier height established at the interface of the most stable stacking patterns of the MS vdWH under investigation. These ndings show the capability to control and modify the properties of the CS, MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and MXY ((X s Y) ¼ S, Se, Te) monolayers, and provide guidelines for the designing of high-performance devices based on MS vdWH.

Computational details
We have used DFT 59 with the empirical dispersion correction of Grimme, 60 and the functionals of Perdew-Burke-Ernzerhof (PBE) 61 and Heyd-Scuseria-Ernzerhof (HSE06) 62 in the Vienna ab initio simulation package (VASP). 63,64 G-point centered 6 Â 6 Â 1 Monkhorst-Pack k-point grids in the rst Brillouin zone and a cutoff energy of 500 eV were used in the PBE functionals for the geometric relaxations until achieving the convergence criterion of 10 À4 eVÅ À1 (10 À5 eV) for forces (energy). The Monkhorst-Pack k-point grids were rened to 12 Â 12 Â 1 for the electronic structure calculations. The converged PBE wave functions were further used for HSE06 calculations, while the k-mesh here was not rened due to the high computational costs. A 25Å vacuum layer thickness was used to avoid interactions between adjacent layers.
We have also performed ab initio molecular dynamics (AIMD) simulations, 65 through the Nose thermostat algorithm at a temperature of 300 K for a total of 6 ps with a time interval of 1 fs to investigate the thermal stabilities of CS-MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and CS-MXY ((X s Y) ¼ S, Se, Te) MS vdWH.
Using the Quantum ESPRESSO package, the Bethe-Salpeter equation (BSE) was also solved using the GW method 66 Table 1 Binding energies (eV) and interlayer distances (Å) of the possible configuration of the CS-MX 2  MXY ((X s Y) ¼ S, Se, Te) vdWH with an alternative order of the chalcogen atoms, see Fig. S2 Table 1, hence recommending the experimental fabrication of the CS-MX 2 and CS-MXY MS vdWH. These values are in the range of the binding energies for other vdWHs. 21,72,73 The calculated interlayer distances (see Table 1) also conrm weak vdW interactions in the stacked layers of the MS vdWHs under investigation. The optimized lattice constants and bond length of the CS-MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and CS-MXY ((X s Y) ¼ S, Se, Te) MS vdWH are presented in Table 2.
Furthermore, we have performed AIMD simulations 74,75 to verify the thermal stability of the MS vdWHs under investigation. There is no structural distortion in the CS-MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and CS-MXY ((X s Y) ¼ S, Se, Te) vdWH aer heating them for 6 ps. The uctuation in the total energy at 0 ps and 6 ps is very small, indicating that these conguration are thermally stable at 300 K, making these systems feasible and they can be obtained easily in future experiments. 70 From AIMD simulations, the geometrical structures before heating (rst row), with uctuating energy (second row) and aer heating (third row) of CS-MoS 2 , and CS-MoSSe in both model-I and -II MS vdWH are presented in Fig. 2.
Using the PBE functional, the calculated electronic band structures of CS-MX 2 and CS-MXY in model-I and -II MS vdWH are calculated and are presented in Fig. 3. It has been shown in ref. 15      density of states (PDOS), see Fig. 4. One can see that in the PDOS, by making the CS-MX 2 and CS-MXY vdWH, the CBM of the MX 2 and MXY layers are shied towards the Fermi level, which is due to the stacking on the CS monolayer, while the main contributions are due to the C-p and S-p orbitals of the CS monolayers (which cross the Fermi level) in the CS-MX 2 and CS-MXY MS vdWH, respectively. An approach in DFT, that hybrid functionals lead to better agreement with experiments than semi-local functionals, is not general, 81 but depends on the considered materials. Therefore, we have also used the HSE06 functional to investigate the electronic band structures of the CS-MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and CS-MXY ((X s Y) ¼ S, Se, Te) vdWH, see Fig. S3. † Using the HSE06 functional, these MS vdWH show similar band structures to the PBE functionals with a small shi in the CBM towards a higher energy.

that the CS monolayer has zero bandgap with indirect
We have also calculated the electrostatic potentials of the CS-MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and CS-MXY ((X s Y) ¼ S, Se, Te) in model-I and -II MS vdWH, see Fig. 5. The electrostatic potential difference (DV), presented in Table 2, lies in the range of À0.76 to À12.28 eV. The MX 2 (MXY) monolayers have deeper electrostatic potentials than that of the CS monolayer in CS-MX 2 (CS-MXY) MS vdWH. This difference in the electrostatic potentials may have a crucial impact on the charge injection and carrier dynamics when these systems are used as electrodes. 82 It should be noted that a large potential difference will signicantly inuence the charge transportation of the 2D MS vdWH. This electrostatic potential at the interface of CS-MX 2 and CS-MXY MS vdWH can successfully reduce the charge carrier recombination and increase the transfer and separation of the induced charge carriers, which enhances the power conversion efficiency. 83 The surface conditions of the material affect the work function due to altering the surface electric eld induced by the distribution of electrons at the interface. 84 The calculated values of the work functions for the CS-MX 2 and CS-MXY MS vdWH lie in the range of 1.46 to 2.71 eV, see Tables 2 and S1, † which show a good response for eld effect transistors (FETs). 85 Using the HSE06 functional, the calculated average electrostatic potential of the CS-MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and CS-MXY ((X s Y) ¼ S, Se, Te) in model-I and -II MS vdWH are presented in Fig. S4 and Table S1. † Charge redistribution and transfer (quantitatively) from one layer to the other layer are investigated by charge density difference and Bader charge analysis using Dr ¼ r   Table 2.
The smaller values of the effective mass (for holes and electrons) indicate that the CS-MX 2 and CS-MXY MS vdWH have high carrier mobility i.e. m ¼ es m* and, hence, are suitable for high performance nanoelectronic devices. From Table 2, one can see that CS-WS 2 and CS-MoSeTe have smaller effective mass (higher carrier mobility) as compared to those of the other vdWH, demonstrating that these heterostructures render promising prospects for nanoelectronic and optoelectronic devices, such as a high efficiency solar cell. In addition, we found that the effective mass of holes is higher than that of electrons, suggesting that these heterostructures can be utilized for hole/electron separation. 87 Using the HSE06 functional, the calculated carrier effective mass of the CS-MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and CS-MXY ((X s Y) ¼ S, Se, Te) in model-I and -II MS vdWH are presented in Table S1. † Interestingly, MS contact led to the formation of a Schottky contact or ohmic contact. We can see from the electronic band structures in Fig. 3 and S2 † that the Fermi levels of the CS-MX 2 (CS-MXY) MS vdWH lie between the CBM and VBM of the    Fig. 6. One can see that F B,p have higher values than F B,n , thus, the CS-MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and CS-MXY ((X s Y) ¼ S, Se, Te) (in both model-I and -II) vdWH form p-type Schottky contacts. These p-type Schottky contacts can be considered to be a promising building block for highperformance photoresponsive optoelectronic devices, 89 p-type electronics, 90 CS-based contacts, 91 and for high-performance electronic devices. 92 While making the CS-MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and CS-MXY ((X s Y) ¼ S, Se, Te) vdWH, there is no chemical bond among CS and MX 2 (MXY) layers, which may create an interface dipole, which can be calculated via the potential step Dr, as presented in Fig. 7. In the case of the SBH of p(n)-type, F B,n ¼ W CS + DV À c (CS-MX2,CS-MXY) (F B,n ¼ I (CS-MX2,CS-MXY) À W CS + DV), where W represents the calculated work function c is the electron affinity and I is the ionization energies of the vdWH and corresponding monolayers. We have calculated the work function and DV, presented in Table 2. The calculated values of F B,n and F B,p with and without considering DV are quite unchanged. Hence, the interface dipole at the CS-MX 2 and CS-MXY vdWH is neglected within the vdW layers. 93 For use in practical applications in optoelectronic and photocatalytic nano devices, we have further calculated the imaginary parts of the dielectric function (3 2 (u) Fig. 8) exhibit an intense absorption peak near the visible region, which suggests the visible light absorption capability of these systems. Fig. S4 † also shows that the 3 2 (u) spectrum of CS is very weak as compared to those of TMDCs and JTMDCs. Furthermore, a slight blueshi is found in the spectra of all MS vdWH compared to those of the isolated monolayers. Fig. 8 also shows that the absorption intensity of the 3 2 (u) spectra for the vdW heterostructures overlaps with those of TMDCs and JTMDCs but is higher than that of the CS monolayer. This indicates the good absorption capability of the constructed heterostructure. 94

Conclusion
Lattice mismatch and the same hexagonal symmetry of the CS (metal) and the MX 2 (M ¼ Mo, W; X ¼ S, Se, Te) and MXY ((X s Y) ¼ S, Se, Te) (semiconductor) monolayers also allow the formation of MS contacts in the form of vdWH. Therefore, using (hybrid) rst principles calculations, we have investigated the electronic band structure, type of Schottky contact and Schottky barrier height established at the interface of the most stable stacking patterns of the CS-MX 2  MS vdWH form p-type Schottky contacts, a promising building block for high-performance photoresponsive optoelectronic devices, p-type electronics, CS-based contacts, and for highperformance electronic devices.

Conflicts of interest
There are no conicts to declare.